The typekit font works fine when I preview the website or publish the website onto the internet.

But inside edge animate where I am doing the building of the website, it just shows the fallback font, which is different enough to cause text to be out of place when viewing the creation in a browser.

I have been told that it is something to do with the settings on my computer. I am using a PC.

Do you have localhost (127.0.0.1) added to your Typekit's settings? I'm surprised that it's working on preview if it's failing on the stage, as one of the likely culprits is often a firewall setup issue.